Hands wraps are surprisingly complex, form what style to how to wrap your hands. I'm going to be covering the different styles of hand wraps.
Regular hand wraps are made of thick cotton and provide a little bit of cushioning as well as binding of your bones in your hand. You might be tempted to hit a heavy bay with just the wraps, but don't. Just put on your pair of boxing gloves before you hit the bag. The trouble with cotton wraps is that they tend to shirk in the dryer. Now, you could hang them up to dry, but that's assuming you have a warm sunny day or another cheap heat source.
Mexican wraps are a blend of cotton and elastic. This allows you to wrap around the individual knuckles more easier. In my experience they will shrink less in the dryer. They are thinner in material, but they are longer so it makes up for it.
I personally like Mexican wraps because I know that I can adequately wraps all parts of the hand: the knuckles, the wrist, and the thumb. Also the sterchy-ness of the wraps allows for more tighter compression and better dispersion across the hands.